Least Common Multiple (LCM) of 137 and 84
The least common multiple (LCM) of 137 and 84 is 11508.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 137 and 84?
First, calculate the GCD of 137 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 84 = 1 remainder 53 |
| 2 | 84 ÷ 53 = 1 remainder 31 |
| 3 | 53 ÷ 31 = 1 remainder 22 |
| 4 | 31 ÷ 22 = 1 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 52 | 5044 |
| 41 and 105 | 4305 |
| 137 and 117 | 16029 |
| 185 and 77 | 14245 |
| 123 and 176 | 21648 |